Turning ability is a factor that determines success in hunting prey and escaping from predators. However, little is understood about the biomechanics of turning at high speeds. We investigated gait characteristics of the cheetah and greyhound while running in a straight line and on curves. Four cheetahs and four greyhounds were filmed running around a 400-m track consisting of two 80-m straights and two bends with a radius of 38 m in a counterclockwise direction. The animals were motivated to run using a lure with speeds of 15–18 m s^-1 We found that the footfall order was fixed during curve running, although it was variable while running straight. Both the cheetahs and greyhounds used the rotatory gallop with the footfall order of right fore, left fore, left hind, and right hind during curve running. The duty factor increased on curves compared with straight running for three out of the four limbs in the greyhounds, but only for the inside hindlimb in the cheetahs. Interlimb coordination varied across running conditions in the cheetahs, but was unchanged in the greyhounds. The results suggest that animals do not use exactly the same strategies to deal with curve running.